This means 5 meters/20 steps = x/1,000 steps. 20 times 50 is 1,000, so 5 times 50 is 250 meters. 5/20 can be also reduced to 1/4 = x/1000. Use cross products rule to get 4x = 1,000. Divided both sides by 4 to get x = 250 meters.
Measures of angles are X = 102° and Y = 78°
Step-by-step explanation:
- Step 1: Let ∠X = 24 + Y. As they are supplementary angles, ∠X + ∠Y = 180°
⇒ 24 + Y + Y = 180
⇒ 2Y = 180 - 24 = 156
⇒ Y = 156/2 = 78°
- Step 2: Find measure of X
⇒ X = 24 + Y = 24 + 78 = 102°
Answer:
Quarterly saving is $709.13
Interest value is $1,817.40
Step-by-step explanation:
A fix Payment for a specified period of time is called annuity. The Compounding of these payment on a specified rate is known as Future value of annuity.
We can calculate the amount of saving in each quarter Formula for Future value of annuity because we already have future value of $16,000
Future value of annuity = FV = P x ( [ 1 + r ]^n - 1 ) / r
Where
FV = $16,000
r = rate of return = 5%
n = number of years = 5 years 4 quarters each year = 20 quarters
Placing Value in the formula
$16,000 = P x ( [ 1 + 5%/4 ]^20 - 1 ) / 5%/4
$16,000 = P x 22.563
P = $16,000 / 22.563 = $709.13
Interest Amount = Future Value - Total Payment = $16,000 - (709.13 x 20) = $1,817.4
Answer:
See explanations below
Step-by-step explanation:
Slope intercept form of the equation is expressed as y = mx+b
m is the slope
b is the intercept
Given the coordinates (4, -11/3) and (1/2, -29/6)
Slope m = -29/6-(-11/3)÷(1/2-4)
m = (-29/6+11/3)÷(-7/2)
m = -29+22/6÷(-7/2)
m = -7/6÷(-7/2)
m = -7/6×2/-7
m = 2/6
m = 1/3
Get the intercept b
Substitute m= 1/3 and (4, -11/3) into y = MX+b
-11/3 = 1/3(4)+b
-11/3 = 4/3+b
b= -11/3-4/3
b= -15/3
b =-5
Get the required equation
y = 1/3 x -5 (slope-intercept form)
Point slope form of the equation is expressed as y-y0 = m(x-x0)
Substituting m = 1/3 and the point (4,-11/3)
x0 = 4
y0 = -11/3
y - (-11/3) = 1/3(x-4)
y+11/3 = 1/3(x-4) (point-slope form)
For standard format
Recall that y = 1/3x - 5
Multiply through by 3
3y = 1/3x(3)-5(3)
3y = x-15
3y-x = -15(standard form)
2/3 x 3/9 =
6/9 x 3/9
18/81=
6/27
therefore, the answer is 6/27